Dispatch

When the reciprocal prices across two markets sum to less than one, there's a locked-in profit sitting between them. Here's how to actually find it.

ARIMA has a reputation for being textbook-dense. Stripped down, it's just three ideas — autoregression, differencing, and moving averages — stacked on top of each other.

Picking (p, d, q) by hand is tedious and easy to get wrong. Auto-ARIMA searches the model space and picks the winner by AIC so you don't have to.

ACF and PACF are the diagnostic step nobody skips if they want an ARIMA model that actually fits — they tell you how many lags a series remembers.

Before you trade a strategy with real money, run it against history first. The FatNarwhal backtester turns an SMA crossover idea into hard numbers on win rate, drawdown, and total return.

New evidence dropped and your gut wants to overreact or ignore it. Bayes' theorem is the actual math for updating a probability the right amount.

The binomial tree prices options the way a decision tree thinks — branch by branch, up move or down move, all the way to expiration.

Fifty years old and still the backbone of the options market. A walkthrough of the Black-Scholes formula, the Greeks it produces, and where the model quietly breaks down.

Being right isn't the same as being well-calibrated. The Brier score is how superforecasters actually measure whether their probabilities are any good.

Pairs trading starts with a question: do two stocks drift together over time, even when neither one is stationary on its own? Cointegration is how you test for it.

One prediction market is one opinion. Blending several into a liquidity-weighted consensus is a sharper estimate than trusting any single platform.

Ten stocks in a portfolio doesn't mean ten independent bets. A correlation matrix shows you how much of your 'diversification' is an illusion.

Every posted price has the house's cut baked in. Stripping the vig is the first step to knowing what odds are actually saying about probability.

Interfaces and fees matter at the margins. The number that actually decides whether you make money over time is expected value — and most active bettors have never calculated it.

Volatility doesn't spread out evenly — it clusters. Calm markets stay calm, wild markets stay wild, and GARCH is the model built to use that pattern.

Is a market trending or fighting its way back to the mean? The Hurst exponent puts a single number on that question, pulled straight from the price history.

Option prices embed a volatility forecast the market is willing to pay for. Backing it out of the price is how you read what the market actually expects.

Most bettors have a process for picking positions and no process for sizing them. The Kelly Criterion gives you the exact fraction of bankroll a real edge is worth risking.

A regression line isn't magic; it's just the best straight line through noisy data. Here's the math behind beta, alpha, and R-squared, and when to trust them.

Markowitz proved there's a mathematically best portfolio for a given level of risk. The efficient frontier isn't theory — you can build it for your own assets right now.

The same event, priced differently on every platform. That spread is either an arb, an edge, or a story — but you can't see it without putting the markets side by side.

Everyone quotes their returns. Almost nobody quotes their risk. Volatility, Sharpe ratio, VaR, and max drawdown — the four numbers that tell you what you actually signed up for.

Most portfolios allocate dollars. Risk parity allocates risk — and the difference changes which assets end up carrying the most weight.

Before you model a time series, you need to know if it's actually going somewhere or just wandering. Stationarity tests are how you find out before the model lies to you.

Before you put on a spread, see the whole shape of it. The payoff tool sums every leg into one profit-and-loss curve so you know your breakevens before you're in the trade.

Most financial models hand you one number and act like that settles it. Monte Carlo hands you ten thousand numbers, and that's the point — a walkthrough of the FatNarwhal Monte Carlo tool and the math behind it.

A deep dive into the current state of the tech sector and what investors should watch for in the coming quarters. Key trends include AI adoption, cloud computing growth, and semiconductor supply chains.

Our analysis of undervalued companies with strong fundamentals. These stocks offer compelling risk-reward profiles for patient investors willing to hold through market volatility.

Breaking down the latest jobs report and what it means for the Federal Reserve's interest rate decisions. Employment remains strong, but there are signs of cooling in certain sectors.

An analysis of Boeing's latest leadership changes and what it means for the aerospace industry. Kelly Ortberg takes the helm at a critical time.